In a large bowl combine ground beef, breadcrumbs, egg, half of the chopped onion, salt, black pepper, and garlic powder. Mix gently until just combined; form into four even patties.
Heat vegetable oil in a large skillet over medium-high heat. Add patties and sear 3 to 4 minutes per side until browned but not fully cooked through. Transfer patties to a plate and set aside.
Reduce heat to medium and add 1 tablespoon butter to the same skillet. Add the remaining chopped onion and cook, stirring, until softened and translucent, about 5 minutes.
Stir in the flour and cook 1 minute to remove the raw flour taste, stirring constantly to form a roux with the onions and butter.
Slowly whisk in the beef broth and milk, scraping up any browned bits from the pan. Add Worcestershire sauce and simmer until the gravy thickens, about 3 to 4 minutes.
Return the browned patties to the skillet, spoon gravy over them, cover, and simmer on low for 8 to 10 minutes until patties are cooked through.
Taste the gravy and adjust seasoning with salt and pepper as needed. If gravy is too thick, stir in a little extra broth or milk to reach desired consistency.
Serve smothered hamburger steaks hot, spooning extra onion gravy over each serving. Enjoy with mashed potatoes, rice, or steamed vegetables.
Notes
Leftovers keep 3 days refrigerated. Reheat gently over low heat and add a splash of broth if needed to loosen the gravy.